Page images
PDF
EPUB

4. It is required to mix several forts of wine at 3s. and 7s gallon, with water, that the mixture may worth 4s. per gallon: How much of each fort mustt mixture confift of?

[blocks in formation]

I

gal. wine, at 35.

Anf. 3 gal. water,
{ ditto at 5s. and 4 ditto at 7 s.

I

CASE II.

When the rates of all the ingredients, the quantivy of tu one of them, and the mean rate of the whole mixture, art given to find the feveral quantities of the rest in proportica to the quantity given.

RULE. Take the differences between each price and the mean rate and place them alternately, as in Cafe r. Then, as the difference standing against that fimple, whose quantity is given, is to that quantity; so is each of the other differences, severally, to the several quantities res quired.

EXAMPLES.

I. A merchant has 40lb. of tea, at 6s. per lb. which he will mix with some at 5s. 8d. fome at 5s. 2d. and fome at 4s. 6d. How much of each fort must he take, to mix with the 40lb. that he may fell the mixture at 5s. 5d. per lb.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

2814

14:40

5s. 2d. 5s. 8d.

}

per lb.

2. How much gold of 16, 20 and 24 carats fine, and how much alloy, must be mixed with wooz. of 18 carats fine, that the composition may be 22 carats fine ? Ans. 10oz. of 16 carats fine, 10 of 20, 170 of 24, and 10 of alloy.

ALTERNATION TOTAL.

CASE III.

When the rates of the feveral ingredients, the quantity to be compounded, and the mean rate of the whole mixture are given to find how much of each fort will make up the quantity.

RULE. Place the differences between the mean rate, and the several prices alternately, as in Case ist. Then, As the sum of the quantities, or differences thus determined, is to the given quantity or whole compofition; so is the difference of each rate, to the required quantity of each rate.

EXAMPLES.

1. Suppose I have 4 forts of currants, at 8d. 12d. 18d. and 22d. per lb.-the worst would not fell and the best were too dear; I therefore concluded to mix izolb. and so much of each fort, as to fell them at 16d. per lb. -How much of each fort must I take?

[blocks in formation]

120

pr.

2. A goldsmith has feveral forts of gold, viz. of 19, 17, 20 and 22 carats fine, and would melt together, of all these forts, so much as may make a mass of

EE2

40oz. 18 carats fine; how much of each fort is r quired ?

Anf. 16oz. 15 carats fine, 4oz. 17, 8oz. 20, and 12oz. of 22 carats fine.

3. How many gallons of water, of no value, must be mixed with wine at 4s per gallon, so as to fill a veffel of 80 gallons, that may be afforded at 2s. 9d. per gallon.

Gal.

[blocks in formation]

When more than one of the fimples are limited.

RULE. Find by Alligation Medial, what will be the rate of a mixture made of the given quantities of the limited simples only; then, consider this as the rate of a limited fimple, whose quantity is the sum of the first given limited simples, from which and the rates of the unlimited simples, by Cafe 2d. calculate the quantity.

EXAMPLE.

How much wine at 4s. 6d. and at 5s. per gallon, must be mixed with 6 gallons at 4s. and 6 gallons at 3s. per gallon, that the mixture may be worth 4s. 4d. per gallon ?

[blocks in formation]

Gal. s. Gal.

As 12: 42::1: 3/6
(per gal.

!

[blocks in formation]

Now, having found the rate of the limited simples, the

question may stand thus: How much wine at 45. 6d. and 5s. per gallon, must be mixed with 12 gallons at 4s. 6d. per gallon, that the mixture may be worth 4s.

3d. per gallon ?

52

[merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

Position is a rule, which by false, or supposed numbers, taken at pleasure, discovers the true ones required. It is divided into two parts; Single and Double.

SINGLE POSITION.

Single Position teaches to refolve those questions, whose results are proportional to their suppositions ; such as those which require the multiplication or divifion of the number fought by any proposed number; or when it is to be increased or diminished by itself a certain propofed number of times.

RULE 1. Take any number and perform the fame operations with it, as are described to be performed in the question.

2.

Then say; as the sum of the errors is to the given sum; fo is the supposed number to the true one required.

PROOF. Add the several parts of the sum together and if it agrees with the sum it is right.

EXAMPLES.

A schoolmaster being asked how many scholars he had, faid if I had as many more as I now have, three quarters as many, half as many, one fourth and one eighth as many, I should then have 435; of what number did his school consist ?

Suppose

Suppose he had 80 As 290: 435 :: 80

As many = 80

80

as many = 60

120

as many = 40 29/0)34800(120 Anf.

120

[blocks in formation]

Proof 435

412

148

2.

A person lent his friend a sum of money unknown, to receive interest for the same at 61. per cent. per annum, simple interest, and at the end of 12 years, received for principal and interest 8601.; what was the fum lent ?

Anf 500l.

3. A, B and C joined their stocks, and gained 3501.; of which A took up a certain sum; B took up four times so much as A, and C eight times so much as B ;

what share of the gain had each ?

Ans.

{

£. s.

99

2

3

A's share.

d. qrs.
I
37 16 9 B's ditto.
302 14 Ο 2 C's ditto.

4. A, B, C and D spent 35s. at a reckoning, and being a little dipped, they agreed that A should pay B, C, and D4; what did each pay in the above proportion?

[blocks in formation]

5. A certain fum of money is to be divided between 5 men in such a manner as that A shall have, BC To, D 20, and E the remainder, which is 40l.; what is the fum ?

[blocks in formation]

Suppose £200 then

++1+2=120.

200-120-80, As, 80: 40 :: 200 : 100, Anf.

« PreviousContinue »